Study 1: Compare the accuracies of two competitive tests without a gold standard. Summary: In population screening or disease diagnosis, multiple diagnostic tests are often conducted on the same subject or sample in order to evaluate the accuracy of these tests and to estimate disease prevalence. Oftentimes, due to economic or ethical concerns, a gold standard may not be readily available, however. The lack of identifiability is a common challenge for estimating test efficacy in this situation. Latent variable models and Bayesian methods have been proposed for estimating the accuracy of diagnostic tests and disease prevalence in the absence of a gold standard. In this work, we extended the previously proposed Bayesian method for binary tests to allow the inclusion of information on covariates by modeling the dependence of prevalence and accuracy on covariates via regression models. As an application, the method was applied to data from a population-based aging study. We combined three popular tests of GFR to estimate the prevalence of impaired kidney function among older adults and to demonstrate that covariates can add important information to the estimation of prevalence and test accuracy. Study 2: Combine the results from multiple tests in a multi-stage screening study. Summary: In studies to ascertain true disease status, a definitive diagnostic test often is too invasive or expensive to be applied to all subjects, in which case a two-phase design is often used. The results for all subjects from the Phase 1 test, which is inexpensive and non-invasive, are used to determine which subjects will receive the gold standard test in a later phase. Analysis restricted only to verified cases leads to verification bias. The multiple phase design has been used in studies of dementia and in the diagnosis and screening of many other diseases, e.g., colorectal and breast cancer. The design usually involves more than two phases. For example, in a three-phase study the prevalent test in Phase 1 usually has high sensitivity, but relatively low specificity;Phase 2 consists of a second application of the screening test or a more confirmatory test;and the test in the final phase is the gold standard. In this paper, we proposed a method of estimating the parameters of test efficacy and the ROC curves for continuous screening tests in a multiple-phase study in the presence of verification bias. The verification process and efficacy of the screening test could also depend on covariates. We evaluated estimates of parameters of test efficacy after adjusting for verification bias, and we compared different schemes for combining the sequential tests using empirical studies. If we assume the people with unverified dementia status as non-demented, we tend to be optimistic about the ROC curve. For example for a subject who is 70 years old with no education, using a cut-off at 75 yields FPR=0.42 and TPR=0.64. If we ignore the verification bias, then FPR=0.39 and TPR=0.96, which over-estimates the specificity. Comparing Figure4 a-d, we see that education level has a remarkable impact on test accuracy if the cut-off of 75 is used, but there is not much difference for different ages. For the subject who is 70 years old and has 10 years of education, the FPR is 0.05 and TPR is 0.30 for the cut-off of 75. So the screening test using the cut-off of 75 has a high sensitivity and relatively low specificity for subjects with a 10-year education. For subjects with low education, both sensitivity and specificity are moderate. In terms of AUC under the ROC curve, the CASI test performed better for subjects with higher education.